Algebraic geometry, derived and noncommutative algebraic geometry, homological algebra, categories of (quasi)coherent sheaves, derived and triangulated categories, mirror symmetry.
Main publications:
D. O. Orlov, “Projective bundles, monoidal transformations, and derived categories of coherent sheaves”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 133–141
D. O. Orlov, “Equivalences of derived categories and $K3$ surfaces”, Algebraic geometry, 7, J. Math. Sci. (New York), 84:5 (1997), 1361–1381 , arXiv: alg-geom/9606006
A. Bondal, D. Orlov, “Reconstruction of a variety from the derived category and groups of autoequivalences”, Compositio Math., 125:3 (2001), 327–344 , arXiv: alg-geom/9712029
D. O. Orlov, “Triangulated Categories of Singularities and D-Branes in Landau–Ginzburg Models”, Proc. Steklov Inst. Math., 246 (2004), 227–248 , arXiv: math/0302304
D. Orlov, “Derived categories of coherent sheaves and triangulated categories of singularities”, Algebra, arithmetic, and geometry, v. II, Progr. Math., 270, Birkhäuser Boston, Inc., 2009, 503–531 , arXiv: math/0503632
V. A. Lunts, D. O. Orlov, “Uniqueness of enhancement for triangulated categories”, J. Amer. Math. Soc., 23:3 (2010), 853–908 , arXiv: 0908.4187
S. Gorchinskiy, D. Orlov, “Geometric phantom categories”, Publ. Math. Inst. Hautes Études Sci., 117:1 (2013), 329–349 , arXiv: 1209.6183
Dmitri Orlov, “Smooth and proper noncommutative schemes and gluing of DG categories”, Adv. Math., 302 (2016), 59–105 , arXiv: 1402.7364
L. A. Borisov, D. O. Orlov, “Equivariant exceptional collections on smooth toric stacks”, Izv. Math., 83:4 (2019), 698–730
2.
D. O. Orlov, “Finite-dimensional DG algebras and their properties”, Russian Math. Surveys, 74:4 (2019), 764–766
3.
Dmitri Orlov, Finite-dimensional differential graded algebras and their geometric realizations, 2019 , 29 pp., arXiv: 1907.08162
4.
V. A. Artamonov, V. M. Buchstaber, È. B. Vinberg, L. V. Kuz'min, Vik. S. Kulikov, V. N. Latyshev, A. V. Mikhalev, A. Yu. Ol'shanskii, D. O. Orlov, A. N. Parshin, D. I. Piontkovskii, Uspekhi Mat. Nauk
2018
5.
D. O. Orlov, “Derived noncommutative schemes, geometric realizations, and finite dimensional algebras”, Russian Math. Surveys, 73:5 (2018), 865–918 , arXiv: 1808.02287
6.
A. A. Beilinson, A. S. Vishik, D. A. Kazhdan, M. M. Kapranov, A. S. Merkurjev, D. O. Orlov, I. A. Panin, A. A. Suslin, N. A. Tyurin, G. B. Shabat, “Vladimir Aleksandrovich Voevodsky (obituary)”, Russian Math. Surveys, 73:3 (2018), 519–531
2016
7.
Dmitri Orlov, “Smooth and proper noncommutative schemes and gluing of DG categories”, Adv. Math., 302 (2016), 59–105 , arXiv: 1402.7364 (cited: 10) (cited: 23) (cited: 25)
8.
D. O. Orlov, “Gluing of categories and Krull–Schmidt partners”, Russian Math. Surveys, 71:3 (2016), 594–596 , arXiv: 1606.00332 (cited: 2) (cited: 3)
9.
Sovremennye problemy matematiki, mekhaniki i matematicheskoi fiziki. II, Sbornik statei, Tr. MIAN, 294, ed. D. O. Orlov, A. G. Sergeev, MAIK «Nauka/Interperiodika», M., 2016 , 327 pp.
10.
V. M. Buchstaber, S. M. Gusein-Zade, M. È. Kazarian, V. V. Kozlov, S. K. Lando, S. P. Novikov, D. O. Orlov, A. G. Khovanskii, “Viktor Anatolevich Vassiliev (on his 60th birthday)”, Russian Math. Surveys, 71:6 (2016), 1153–1157
2015
11.
D. O. Orlov, “Geometric Realizations of Quiver Algebras”, Proc. Steklov Inst. Math., 290 (2015), 70–83 , arXiv: 1503.03174 (cited: 12) (cited: 1) (cited: 1) (cited: 13)
12.
Sovremennye problemy matematiki, mekhaniki i matematicheskoi fiziki, Sbornik statei, Tr. MIAN, 290, ed. D. O. Orlov, A. G. Sergeev, MAIK «Nauka/Interperiodika», M., 2015 , 343 pp.
2013
13.
A. Canonaco, D. Orlov, P. Stellari, “Does full imply faithful?”, J. Noncommut. Geom., 7:2 (2013), 357–371 , arXiv: 1101.5931 (cited: 6) (cited: 1) (cited: 6)
M. Abouzaid, D. Auroux, A. I. Efimov, L. Katzarkov, D. Orlov, “Homological mirror symmetry for punctured spheres”, J. Amer. Math. Soc., 26:4 (2013), 1051–1083 , arXiv: 1103.4322 (cited: 26) (cited: 6) (cited: 22)
16.
V. Alexeev, D. Orlov, “Derived categories of Burniat surfaces and exceptional collections”, Math. Ann., 357:2 (2013), 743–759 , arXiv: 1208.4348 (cited: 22) (cited: 7) (cited: 21)
17.
S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarkhin, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, V. L. Popov, A. G. Sergeev, I. R. Shafarevich, “Aleksei Nikolaevich Parshin (on his 70th birthday)”, Russian Math. Surveys, 68:1 (2013), 189–197
D. Orlov, “Landau–Ginzburg models, D-branes, and Mirror Symmetry”, Matemática Contemporânea, 41 (2012), 75–112 , arXiv: 1111.2962
2011
20.
D. Orlov, “Formal completions and idempotent completions of triangulated categories of singularities”, Adv. Math., 226:1 (2011), 206–217 , arXiv: 0901.1859 (cited: 33) (cited: 20) (cited: 35)
21.
A. I. Efimov, V. A. Lunts, D. O. Orlov, “Deformation theory of objects in homotopy and derived categories III: Abelian categories.”, Adv. Math., 226:5 (2011), 3857–3911 , arXiv: math/0702840 (cited: 5) (cited: 2) (cited: 6)
2010
22.
A. I. Efimov, V. A. Lunts, D. O. Orlov, “Deformation theory of objects in homotopy and derived categories. II. Pro-representability of the deformation functor”, Adv. Math., 224:1 (2010), 45–102. , arXiv: math/0702839 (cited: 6) (cited: 3) (cited: 7)
23.
V. A. Lunts, D. O. Orlov, “Uniqueness of enhancement for triangulated categories”, J. Amer. Math. Soc., 23:3 (2010), 853–908 , arXiv: 0908.4187 (cited: 91) (cited: 50) (cited: 90)
24.
F. A. Bogomolov, Yu. G. Zarhin, Vik. S. Kulikov, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, M. Reid, I. A. Cheltsov, “Vyacheslav Vladimirovich Shokurov (on his 60th birthday)”, Russian Math. Surveys, 65:6 (2010), 1193–1198
2009
25.
A. I. Efimov, V. A. Lunts, D. O. Orlov, “Deformation theory of objects in homotopy and derived categories. I. General theory”, Adv. Math., 222:2 (2009), 359–401 , arXiv: math/0702838 (cited: 10) (cited: 6) (cited: 8)
26.
Dmitri Orlov, “Remarks on generators and dimensions of triangulated categories”, Mosc. Math. J., 9:1 (2009), 143–149 , arXiv: 0804.1163 (cited: 31) (cited: 37)
27.
A. Kapustin, L. Katzarkov, D. Orlov, M. Yotov, “Homological Mirror Symmetry for manifolds of general type”, Cent. Eur. J. Math., 7:4 (2009), 571–605 , arXiv: 1004.0129 (cited: 21) (cited: 14) (cited: 25)
28.
D. Orlov, “Derived categories of coherent sheaves and triangulated categories of singularities”, Algebra, arithmetic, and geometry, v. II, Progr. Math., 270, Birkhäuser Boston, Inc., 2009, 503–531 , arXiv: math/0503632 (cited: 131) (cited: 140)
29.
F. A. Bogomolov, Vik. S. Kulikov, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, A. V. Pukhlikov, M. Reid, I. R. Shafarevich, V. V. Shokurov, “Vasilii Alekseevich Iskovskikh (obituary)”, Russian Math. Surveys, 64:5 (2009), 939–946
2008
30.
D. Auroux, L. Katzarkov, D. Orlov, “Mirror symmetry for weighted projective planes and their noncommutative deformations”, Ann. of Math. (2), 167:3 (2008), 867–943 , arXiv: math/0404281 (cited: 77) (cited: 37) (cited: 76)
2007
31.
D. Orlov, A. Vishik, V. Voevodsky, “An exact sequence for $K^{M}_{*}/2$ with applications to quadratic forms”, Ann. of Math. (2), 165:1 (2007), 1–13 , arXiv: math/0101023 (cited: 75) (cited: 50) (cited: 74)
32.
V. A. Vassiliev, Yu. G. Zarhin, V. A. Iskovskikh, D. B. Kaledin, Vik. S. Kulikov, Yu. I. Manin, D. O. Orlov, A. N. Parshin, I. R. Shafarevich, “Fedor Alekseevich Bogomolov (on his 60th birthday)”, Russian Math. Surveys, 62:6 (2007), 1233–1237
2006
33.
D. Auroux, L. Katzarkov, D. Orlov, “Mirror symmetry for del Pezzo surfaces: vanishing cycles and coherent sheaves”, Invent. Math., 166:3 (2006), 537–582 , arXiv: math/0506166 (cited: 63) (cited: 36) (cited: 59)
34.
D. O. Orlov, “Triangulated categories of singularities and equivalences between Landau–Ginzburg models”, Sb. Math., 197:12 (2006), 1827–1840 , arXiv: math/0503630 (cited: 49) (cited: 24) (cited: 24) (cited: 52)
2005
35.
D. O. Orlov, “Derived categories of coherent sheaves and motives”, Russian Math. Surveys, 60:6 (2005), 1242–1244 , arXiv: math/0512620 (cited: 20) (cited: 6) (cited: 6) (cited: 16)
2004
36.
A. N. Kapustin, D. O. Orlov, “Lectures on mirror symmetry, derived categories, and D-branes”, Russian Math. Surveys, 59:5 (2004), 907–940 , arXiv: math/0308173 (cited: 4) (cited: 4) (cited: 15)
37.
D. O. Orlov, “Triangulated Categories of Singularities and D-Branes in Landau–Ginzburg Models”, Proc. Steklov Inst. Math., 246 (2004), 227–248 , arXiv: math/0302304
38.
I. R. Shafarevich, D. O. Orlov, N. A. Tyurin, “Preface”, Proc. Steklov Inst. Math., 246 (2004), 1–2
2003
39.
A. Kapustin, D. Orlov, “Remarks on A-branes, mirror symmetry, and the Fukaya category”, J. Geom. Phys., 48:1 (2003), 84–99 , arXiv: hep-th/0109098 (cited: 56) (cited: 51) (cited: 70)
40.
A. Kapustin, D. Orlov, “Vertex algebras, mirror symmetry, and D-branes: the case of complex tori”, Comm. Math. Phys., 233:1 (2003), 79–136 , arXiv: hep-th/0010293 (cited: 36) (cited: 30) (cited: 48)
41.
D. O. Orlov, “Quasi-coherent sheaves in commutative and non-commutative geometry”, Izv. Math., 67:3 (2003), 535–554 (cited: 4) (cited: 2) (cited: 2)
42.
D. O. Orlov, “Derived categories of coherent sheaves and equivalences between them”, Russian Math. Surveys, 58:3 (2003), 511–591 (cited: 48) (cited: 22) (cited: 48)
43.
F. A. Bogomolov, A. L. Gorodentsev, V. A. Iskovskikh, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, V. Ya. Pidstrigach, A. S. Tikhomirov, N. A. Tyurin, I. R. Shafarevich, “Andrei Nikolaevich Tyurin (obituary)”, Russian Math. Surveys, 58:3 (2003), 597–605
2002
44.
A. Bondal, D. Orlov, “Derived categories of coherent sheaves”, Proceedings of the International Congress of Mathematicians (Beijing, 2002), v. II, Higher Ed. Press, Beijing, 2002, 47–56 , arXiv: math/0206295
45.
D. O. Orlov, “Derived categories of coherent sheaves on Abelian varieties and equivalences between them”, Izv. Math., 66:3 (2002), 569–594 , arXiv: alg-geom/9712017 (cited: 25) (cited: 56)
2001
46.
A. Kapustin, A. Kuznetsov, D. Orlov, “Noncommutative instantons and twistor transform”, Comm. Math. Phys., 221:2 (2001), 385–432 , arXiv: hep-th/0002193 (cited: 70) (cited: 57) (cited: 74)
47.
V. Golyshev, V. Lunts, D. Orlov, “Mirror symmetry for abelian varieties”, J. Algebraic Geom., 10:3 (2001), 433–496 , arXiv: math/9812003 (cited: 17) (cited: 15) (cited: 21)
48.
A. Bondal, D. Orlov, “Reconstruction of a variety from the derived category and groups of autoequivalences”, Compositio Math., 125:3 (2001), 327–344 , arXiv: alg-geom/9712029 (cited: 119) (cited: 72) (cited: 124)
1997
49.
D. O. Orlov, “Equivalences of derived categories and $K3$ surfaces”, Algebraic geometry, 7, J. Math. Sci. (New York), 84:5 (1997), 1361–1381 , arXiv: alg-geom/9606006 (cited: 179)
S. A. Kuleshov, D. O. Orlov, “Exceptional sheaves on del Pezzo surfaces”, Russian Acad. Sci. Izv. Math., 44:3 (1995), 479–513 (cited: 41) (cited: 42)
1993
52.
D. O. Orlov, “Projective bundles, monoidal transformations, and derived categories of coherent sheaves”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 133–141 (cited: 112) (cited: 110)
1991
53.
D. O. Orlov, “Exceptional set of vector bundles on the variety $V_5$”, Moscow Univ. Math. Bull., 46:5 (1991), 48–50 (cited: 22)
1989
54.
L. V. Katsarkov, D. O. Orlov, “Prym varieties of hyperelliptic curves and their applications to nonlinear equations”, Moscow Univ. Math. Bull., 44:2 (1989), 65–69
Geometric realisations of algebraic objects D. O. Orlov International conference ''Algebra, algebraic geometry and number theory'' dedicated to the memory of academician Igor Rostislavovich Shafarevich June 13, 2018 16:20
Geometric phantom categories D. O. Orlov Seminar "Complex analysis in several variables" (Vitushkin Seminar) October 31, 2012 16:45
46.
Opening ceremony D. O. Orlov Annual memorial conference dedicated to the memory of Andrei Nikolaevich Tyurin (24.02.1940–27.10.2002) "Algebraic and Differential Geometry of Andrei Tyurin" October 24, 2012 11:00
Open ceremony D. O. Orlov, A. G. Sergeev, A. N. Parshin, M. Reid, V. V. Shokurov International conference "Geometry of Algebraic Varieties" dedicated to the memory of Vasily Alexeevich Iskovskikh June 29, 2009 10:00
Mirror symmetry from the mathematical point of view Dmitry Orlov General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences October 9, 2006
Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Tr. Mat. Inst. Steklova, 294, ed. D. O. Orlov, A. G. Sergeev, 2016, 327 с. http://mi.mathnet.ru/book1618
Modern problems of mathematics, mechanics, and mathematical physics, Collected papers, Tr. Mat. Inst. Steklova, 290, ed. D. O. Orlov, A. G. Sergeev, 2015, 343 с. http://mi.mathnet.ru/book1589